1 Data preparation

1.1 Outline

  • Load scripts: loads libraries and useful scripts used in the analyses; all .R files contained in scripts at the root of the factory are automatically loaded

  • Load data: imports datasets, and may contain some ad hoc changes to the data such as specific data cleaning (not used in other reports), new variables used in the analyses, etc.

1.2 Load packages


library(reportfactory)
library(here)
library(rio) 
library(tidyverse)
library(incidence)
library(distcrete)
library(epitrix)
library(earlyR)
library(projections)
library(linelist)
library(remotes)
library(janitor)
library(kableExtra)
library(DT)
library(cyphr)
library(chngpt)
library(lubridate)
library(ggpubr)
library(ggnewscale)

1.3 Load scripts

These scripts will load:

  • all scripts stored as .R files inside /scripts/
  • all scripts stored as .R files inside /src/

These scripts also contain routines to access the latest clean encrypted data (see next section).


reportfactory::rfh_load_scripts()

1.4 Load clean data

We import the latest NHS pathways data:


x <- import_pathways() %>%
  as_tibble()
x
## # A tibble: 163,936 x 11
##    site_type date       sex   age   ccg_code ccg_name count postcode nhs_region
##    <chr>     <date>     <chr> <chr> <chr>    <chr>    <int> <chr>    <chr>     
##  1 111       2020-03-18 fema… 70-1… e380000… nhs_cas…     6 ss67qf   East of E…
##  2 111       2020-03-18 fema… 70-1… e380000… nhs_cho…     1 pr266tt  North West
##  3 111       2020-03-18 fema… 70-1… e380000… nhs_dor…     5 dt11tg   South West
##  4 111       2020-03-18 fema… 70-1… e380000… nhs_dud…     5 dy51ru   Midlands  
##  5 111       2020-03-18 fema… 70-1… e380000… nhs_eas…     2 de142wf  Midlands  
##  6 111       2020-03-18 fema… 70-1… e380000… nhs_hul…     4 hu11uy   North Eas…
##  7 111       2020-03-18 fema… 70-1… e380000… nhs_har…     1 ha13aw   London    
##  8 111       2020-03-18 fema… 70-1… e380000… nhs_ham…     1 dl62uu   North Eas…
##  9 111       2020-03-18 fema… 70-1… e380000… nhs_gre…     2 se186nd  London    
## 10 111       2020-03-18 fema… 19-69 w110000… null         1 NA       NA        
## # … with 163,926 more rows, and 2 more variables: day <int>, weekday <fct>

We also import demographics data for NHS regions in England, used later in our analysis:


path <- here::here("data", "csv", "nhs_region_population_2018.csv")
nhs_region_pop <- rio::import(path) %>%
  mutate(nhs_region = str_to_title(gsub("_"," ",nhs_region)))

nhs_region_pop$nhs_region <- gsub(" Of ", " of ", nhs_region_pop$nhs_region)
nhs_region_pop$nhs_region <- gsub(" And ", " and ", nhs_region_pop$nhs_region)
nhs_region_pop
##                  nhs_region variable      value
## 1                North West     0-18 0.22538599
## 2  North East and Yorkshire     0-18 0.21876449
## 3                  Midlands     0-18 0.22564656
## 4           East of England     0-18 0.22810783
## 5                    London     0-18 0.23764782
## 6                South East     0-18 0.22458811
## 7                South West     0-18 0.20799797
## 8                North West    19-69 0.64274078
## 9  North East and Yorkshire    19-69 0.64437753
## 10                 Midlands    19-69 0.63876675
## 11          East of England    19-69 0.63034229
## 12                   London    19-69 0.67820084
## 13               South East    19-69 0.63267336
## 14               South West    19-69 0.63176131
## 15               North West   70-120 0.13187323
## 16 North East and Yorkshire   70-120 0.13685797
## 17                 Midlands   70-120 0.13558669
## 18          East of England   70-120 0.14154988
## 19                   London   70-120 0.08415135
## 20               South East   70-120 0.14273853
## 21               South West   70-120 0.16024072

Finally, we import publically available deaths per NHS region:


dth <- import_deaths() %>%
  mutate(nhs_region = str_to_title(gsub("_"," ",nhs_region)))

#truncation to account for reporting delay
delay_max <- 21

dth$nhs_region <- gsub(" Of ", " of ", dth$nhs_region)
dth$nhs_region <- gsub(" And ", " and ", dth$nhs_region)
dth
##     date_report               nhs_region deaths
## 1    2020-03-01          East of England      0
## 2    2020-03-02          East of England      1
## 3    2020-03-03          East of England      0
## 4    2020-03-04          East of England      0
## 5    2020-03-05          East of England      0
## 6    2020-03-06          East of England      1
## 7    2020-03-07          East of England      0
## 8    2020-03-08          East of England      0
## 9    2020-03-09          East of England      1
## 10   2020-03-10          East of England      0
## 11   2020-03-11          East of England      0
## 12   2020-03-12          East of England      0
## 13   2020-03-13          East of England      1
## 14   2020-03-14          East of England      2
## 15   2020-03-15          East of England      2
## 16   2020-03-16          East of England      1
## 17   2020-03-17          East of England      1
## 18   2020-03-18          East of England      5
## 19   2020-03-19          East of England      4
## 20   2020-03-20          East of England      2
## 21   2020-03-21          East of England     11
## 22   2020-03-22          East of England     12
## 23   2020-03-23          East of England     11
## 24   2020-03-24          East of England     19
## 25   2020-03-25          East of England     26
## 26   2020-03-26          East of England     36
## 27   2020-03-27          East of England     38
## 28   2020-03-28          East of England     28
## 29   2020-03-29          East of England     43
## 30   2020-03-30          East of England     45
## 31   2020-03-31          East of England     70
## 32   2020-04-01          East of England     62
## 33   2020-04-02          East of England     64
## 34   2020-04-03          East of England     80
## 35   2020-04-04          East of England     71
## 36   2020-04-05          East of England     76
## 37   2020-04-06          East of England     71
## 38   2020-04-07          East of England     93
## 39   2020-04-08          East of England    111
## 40   2020-04-09          East of England     87
## 41   2020-04-10          East of England     74
## 42   2020-04-11          East of England     92
## 43   2020-04-12          East of England    101
## 44   2020-04-13          East of England     78
## 45   2020-04-14          East of England     61
## 46   2020-04-15          East of England     82
## 47   2020-04-16          East of England     74
## 48   2020-04-17          East of England     86
## 49   2020-04-18          East of England     64
## 50   2020-04-19          East of England     67
## 51   2020-04-20          East of England     67
## 52   2020-04-21          East of England     75
## 53   2020-04-22          East of England     67
## 54   2020-04-23          East of England     49
## 55   2020-04-24          East of England     66
## 56   2020-04-25          East of England     54
## 57   2020-04-26          East of England     48
## 58   2020-04-27          East of England     46
## 59   2020-04-28          East of England     58
## 60   2020-04-29          East of England     32
## 61   2020-04-30          East of England     45
## 62   2020-05-01          East of England     49
## 63   2020-05-02          East of England     29
## 64   2020-05-03          East of England     41
## 65   2020-05-04          East of England     19
## 66   2020-05-05          East of England     36
## 67   2020-05-06          East of England     31
## 68   2020-05-07          East of England     33
## 69   2020-05-08          East of England     33
## 70   2020-05-09          East of England     29
## 71   2020-05-10          East of England     22
## 72   2020-05-11          East of England     18
## 73   2020-05-12          East of England     21
## 74   2020-05-13          East of England     27
## 75   2020-05-14          East of England     26
## 76   2020-05-15          East of England     19
## 77   2020-05-16          East of England     26
## 78   2020-05-17          East of England     17
## 79   2020-05-18          East of England     25
## 80   2020-05-19          East of England     15
## 81   2020-05-20          East of England     26
## 82   2020-05-21          East of England     21
## 83   2020-05-22          East of England     13
## 84   2020-05-23          East of England     12
## 85   2020-05-24          East of England     17
## 86   2020-05-25          East of England     25
## 87   2020-05-26          East of England     14
## 88   2020-05-27          East of England     12
## 89   2020-05-28          East of England     17
## 90   2020-05-29          East of England     16
## 91   2020-05-30          East of England      9
## 92   2020-05-31          East of England      8
## 93   2020-06-01          East of England     17
## 94   2020-06-02          East of England     14
## 95   2020-06-03          East of England     10
## 96   2020-06-04          East of England      7
## 97   2020-06-05          East of England     12
## 98   2020-06-06          East of England      5
## 99   2020-06-07          East of England      9
## 100  2020-06-08          East of England      5
## 101  2020-06-09          East of England      6
## 102  2020-06-10          East of England      8
## 103  2020-06-11          East of England      1
## 104  2020-06-12          East of England      9
## 105  2020-06-13          East of England      5
## 106  2020-06-14          East of England      4
## 107  2020-06-15          East of England      8
## 108  2020-06-16          East of England      3
## 109  2020-06-17          East of England      7
## 110  2020-06-18          East of England      4
## 111  2020-06-19          East of England      7
## 112  2020-06-20          East of England      3
## 113  2020-06-21          East of England      3
## 114  2020-06-22          East of England      6
## 115  2020-06-23          East of England      4
## 116  2020-06-24          East of England      4
## 117  2020-06-25          East of England      1
## 118  2020-06-26          East of England      4
## 119  2020-06-27          East of England      5
## 120  2020-06-28          East of England      5
## 121  2020-06-29          East of England      4
## 122  2020-06-30          East of England      0
## 123  2020-03-01                   London      0
## 124  2020-03-02                   London      0
## 125  2020-03-03                   London      0
## 126  2020-03-04                   London      0
## 127  2020-03-05                   London      0
## 128  2020-03-06                   London      1
## 129  2020-03-07                   London      0
## 130  2020-03-08                   London      0
## 131  2020-03-09                   London      1
## 132  2020-03-10                   London      0
## 133  2020-03-11                   London      6
## 134  2020-03-12                   London      6
## 135  2020-03-13                   London     10
## 136  2020-03-14                   London     14
## 137  2020-03-15                   London     10
## 138  2020-03-16                   London     15
## 139  2020-03-17                   London     23
## 140  2020-03-18                   London     27
## 141  2020-03-19                   London     25
## 142  2020-03-20                   London     44
## 143  2020-03-21                   London     49
## 144  2020-03-22                   London     54
## 145  2020-03-23                   London     63
## 146  2020-03-24                   London     87
## 147  2020-03-25                   London    113
## 148  2020-03-26                   London    129
## 149  2020-03-27                   London    130
## 150  2020-03-28                   London    122
## 151  2020-03-29                   London    146
## 152  2020-03-30                   London    149
## 153  2020-03-31                   London    181
## 154  2020-04-01                   London    202
## 155  2020-04-02                   London    191
## 156  2020-04-03                   London    196
## 157  2020-04-04                   London    230
## 158  2020-04-05                   London    195
## 159  2020-04-06                   London    197
## 160  2020-04-07                   London    220
## 161  2020-04-08                   London    238
## 162  2020-04-09                   London    206
## 163  2020-04-10                   London    170
## 164  2020-04-11                   London    178
## 165  2020-04-12                   London    158
## 166  2020-04-13                   London    166
## 167  2020-04-14                   London    144
## 168  2020-04-15                   London    142
## 169  2020-04-16                   London    139
## 170  2020-04-17                   London    100
## 171  2020-04-18                   London    101
## 172  2020-04-19                   London    103
## 173  2020-04-20                   London     95
## 174  2020-04-21                   London     94
## 175  2020-04-22                   London    109
## 176  2020-04-23                   London     77
## 177  2020-04-24                   London     71
## 178  2020-04-25                   London     58
## 179  2020-04-26                   London     53
## 180  2020-04-27                   London     51
## 181  2020-04-28                   London     43
## 182  2020-04-29                   London     44
## 183  2020-04-30                   London     40
## 184  2020-05-01                   London     41
## 185  2020-05-02                   London     41
## 186  2020-05-03                   London     36
## 187  2020-05-04                   London     30
## 188  2020-05-05                   London     25
## 189  2020-05-06                   London     37
## 190  2020-05-07                   London     37
## 191  2020-05-08                   London     30
## 192  2020-05-09                   London     23
## 193  2020-05-10                   London     26
## 194  2020-05-11                   London     18
## 195  2020-05-12                   London     18
## 196  2020-05-13                   London     16
## 197  2020-05-14                   London     20
## 198  2020-05-15                   London     18
## 199  2020-05-16                   London     14
## 200  2020-05-17                   London     15
## 201  2020-05-18                   London      9
## 202  2020-05-19                   London     14
## 203  2020-05-20                   London     19
## 204  2020-05-21                   London     12
## 205  2020-05-22                   London     10
## 206  2020-05-23                   London      6
## 207  2020-05-24                   London      7
## 208  2020-05-25                   London      9
## 209  2020-05-26                   London     13
## 210  2020-05-27                   London      7
## 211  2020-05-28                   London      8
## 212  2020-05-29                   London      7
## 213  2020-05-30                   London     12
## 214  2020-05-31                   London      6
## 215  2020-06-01                   London     10
## 216  2020-06-02                   London      7
## 217  2020-06-03                   London      6
## 218  2020-06-04                   London      8
## 219  2020-06-05                   London      4
## 220  2020-06-06                   London      0
## 221  2020-06-07                   London      5
## 222  2020-06-08                   London      5
## 223  2020-06-09                   London      4
## 224  2020-06-10                   London      7
## 225  2020-06-11                   London      5
## 226  2020-06-12                   London      3
## 227  2020-06-13                   London      3
## 228  2020-06-14                   London      2
## 229  2020-06-15                   London      1
## 230  2020-06-16                   London      2
## 231  2020-06-17                   London      1
## 232  2020-06-18                   London      2
## 233  2020-06-19                   London      3
## 234  2020-06-20                   London      3
## 235  2020-06-21                   London      4
## 236  2020-06-22                   London      2
## 237  2020-06-23                   London      0
## 238  2020-06-24                   London      3
## 239  2020-06-25                   London      3
## 240  2020-06-26                   London      2
## 241  2020-06-27                   London      1
## 242  2020-06-28                   London      1
## 243  2020-06-29                   London      2
## 244  2020-06-30                   London      0
## 245  2020-03-01                 Midlands      0
## 246  2020-03-02                 Midlands      0
## 247  2020-03-03                 Midlands      1
## 248  2020-03-04                 Midlands      0
## 249  2020-03-05                 Midlands      0
## 250  2020-03-06                 Midlands      0
## 251  2020-03-07                 Midlands      0
## 252  2020-03-08                 Midlands      3
## 253  2020-03-09                 Midlands      1
## 254  2020-03-10                 Midlands      0
## 255  2020-03-11                 Midlands      2
## 256  2020-03-12                 Midlands      6
## 257  2020-03-13                 Midlands      5
## 258  2020-03-14                 Midlands      4
## 259  2020-03-15                 Midlands      5
## 260  2020-03-16                 Midlands     11
## 261  2020-03-17                 Midlands      8
## 262  2020-03-18                 Midlands     13
## 263  2020-03-19                 Midlands      8
## 264  2020-03-20                 Midlands     28
## 265  2020-03-21                 Midlands     13
## 266  2020-03-22                 Midlands     31
## 267  2020-03-23                 Midlands     33
## 268  2020-03-24                 Midlands     41
## 269  2020-03-25                 Midlands     48
## 270  2020-03-26                 Midlands     64
## 271  2020-03-27                 Midlands     72
## 272  2020-03-28                 Midlands     89
## 273  2020-03-29                 Midlands     92
## 274  2020-03-30                 Midlands     90
## 275  2020-03-31                 Midlands    123
## 276  2020-04-01                 Midlands    140
## 277  2020-04-02                 Midlands    142
## 278  2020-04-03                 Midlands    124
## 279  2020-04-04                 Midlands    151
## 280  2020-04-05                 Midlands    164
## 281  2020-04-06                 Midlands    140
## 282  2020-04-07                 Midlands    123
## 283  2020-04-08                 Midlands    186
## 284  2020-04-09                 Midlands    139
## 285  2020-04-10                 Midlands    127
## 286  2020-04-11                 Midlands    142
## 287  2020-04-12                 Midlands    139
## 288  2020-04-13                 Midlands    120
## 289  2020-04-14                 Midlands    116
## 290  2020-04-15                 Midlands    147
## 291  2020-04-16                 Midlands    102
## 292  2020-04-17                 Midlands    118
## 293  2020-04-18                 Midlands    115
## 294  2020-04-19                 Midlands     92
## 295  2020-04-20                 Midlands    107
## 296  2020-04-21                 Midlands     86
## 297  2020-04-22                 Midlands     78
## 298  2020-04-23                 Midlands    103
## 299  2020-04-24                 Midlands     79
## 300  2020-04-25                 Midlands     72
## 301  2020-04-26                 Midlands     81
## 302  2020-04-27                 Midlands     74
## 303  2020-04-28                 Midlands     68
## 304  2020-04-29                 Midlands     53
## 305  2020-04-30                 Midlands     56
## 306  2020-05-01                 Midlands     64
## 307  2020-05-02                 Midlands     51
## 308  2020-05-03                 Midlands     52
## 309  2020-05-04                 Midlands     61
## 310  2020-05-05                 Midlands     59
## 311  2020-05-06                 Midlands     59
## 312  2020-05-07                 Midlands     48
## 313  2020-05-08                 Midlands     34
## 314  2020-05-09                 Midlands     37
## 315  2020-05-10                 Midlands     42
## 316  2020-05-11                 Midlands     33
## 317  2020-05-12                 Midlands     45
## 318  2020-05-13                 Midlands     40
## 319  2020-05-14                 Midlands     37
## 320  2020-05-15                 Midlands     40
## 321  2020-05-16                 Midlands     34
## 322  2020-05-17                 Midlands     31
## 323  2020-05-18                 Midlands     34
## 324  2020-05-19                 Midlands     34
## 325  2020-05-20                 Midlands     36
## 326  2020-05-21                 Midlands     32
## 327  2020-05-22                 Midlands     27
## 328  2020-05-23                 Midlands     34
## 329  2020-05-24                 Midlands     19
## 330  2020-05-25                 Midlands     26
## 331  2020-05-26                 Midlands     33
## 332  2020-05-27                 Midlands     29
## 333  2020-05-28                 Midlands     28
## 334  2020-05-29                 Midlands     20
## 335  2020-05-30                 Midlands     20
## 336  2020-05-31                 Midlands     22
## 337  2020-06-01                 Midlands     20
## 338  2020-06-02                 Midlands     22
## 339  2020-06-03                 Midlands     24
## 340  2020-06-04                 Midlands     16
## 341  2020-06-05                 Midlands     21
## 342  2020-06-06                 Midlands     20
## 343  2020-06-07                 Midlands     17
## 344  2020-06-08                 Midlands     16
## 345  2020-06-09                 Midlands     18
## 346  2020-06-10                 Midlands     15
## 347  2020-06-11                 Midlands     13
## 348  2020-06-12                 Midlands     12
## 349  2020-06-13                 Midlands      6
## 350  2020-06-14                 Midlands     18
## 351  2020-06-15                 Midlands     12
## 352  2020-06-16                 Midlands     14
## 353  2020-06-17                 Midlands     10
## 354  2020-06-18                 Midlands     14
## 355  2020-06-19                 Midlands      9
## 356  2020-06-20                 Midlands     14
## 357  2020-06-21                 Midlands     12
## 358  2020-06-22                 Midlands     12
## 359  2020-06-23                 Midlands     17
## 360  2020-06-24                 Midlands     13
## 361  2020-06-25                 Midlands     15
## 362  2020-06-26                 Midlands      5
## 363  2020-06-27                 Midlands      3
## 364  2020-06-28                 Midlands      5
## 365  2020-06-29                 Midlands      4
## 366  2020-06-30                 Midlands      0
## 367  2020-03-01 North East and Yorkshire      0
## 368  2020-03-02 North East and Yorkshire      0
## 369  2020-03-03 North East and Yorkshire      0
## 370  2020-03-04 North East and Yorkshire      0
## 371  2020-03-05 North East and Yorkshire      0
## 372  2020-03-06 North East and Yorkshire      0
## 373  2020-03-07 North East and Yorkshire      0
## 374  2020-03-08 North East and Yorkshire      0
## 375  2020-03-09 North East and Yorkshire      0
## 376  2020-03-10 North East and Yorkshire      0
## 377  2020-03-11 North East and Yorkshire      0
## 378  2020-03-12 North East and Yorkshire      0
## 379  2020-03-13 North East and Yorkshire      0
## 380  2020-03-14 North East and Yorkshire      0
## 381  2020-03-15 North East and Yorkshire      2
## 382  2020-03-16 North East and Yorkshire      3
## 383  2020-03-17 North East and Yorkshire      1
## 384  2020-03-18 North East and Yorkshire      2
## 385  2020-03-19 North East and Yorkshire      6
## 386  2020-03-20 North East and Yorkshire      5
## 387  2020-03-21 North East and Yorkshire      6
## 388  2020-03-22 North East and Yorkshire      7
## 389  2020-03-23 North East and Yorkshire      9
## 390  2020-03-24 North East and Yorkshire      8
## 391  2020-03-25 North East and Yorkshire     18
## 392  2020-03-26 North East and Yorkshire     21
## 393  2020-03-27 North East and Yorkshire     28
## 394  2020-03-28 North East and Yorkshire     35
## 395  2020-03-29 North East and Yorkshire     38
## 396  2020-03-30 North East and Yorkshire     64
## 397  2020-03-31 North East and Yorkshire     60
## 398  2020-04-01 North East and Yorkshire     67
## 399  2020-04-02 North East and Yorkshire     74
## 400  2020-04-03 North East and Yorkshire    100
## 401  2020-04-04 North East and Yorkshire    105
## 402  2020-04-05 North East and Yorkshire     92
## 403  2020-04-06 North East and Yorkshire     96
## 404  2020-04-07 North East and Yorkshire    102
## 405  2020-04-08 North East and Yorkshire    107
## 406  2020-04-09 North East and Yorkshire    111
## 407  2020-04-10 North East and Yorkshire    117
## 408  2020-04-11 North East and Yorkshire     98
## 409  2020-04-12 North East and Yorkshire     84
## 410  2020-04-13 North East and Yorkshire     94
## 411  2020-04-14 North East and Yorkshire    107
## 412  2020-04-15 North East and Yorkshire     96
## 413  2020-04-16 North East and Yorkshire    103
## 414  2020-04-17 North East and Yorkshire     88
## 415  2020-04-18 North East and Yorkshire     95
## 416  2020-04-19 North East and Yorkshire     88
## 417  2020-04-20 North East and Yorkshire    100
## 418  2020-04-21 North East and Yorkshire     76
## 419  2020-04-22 North East and Yorkshire     84
## 420  2020-04-23 North East and Yorkshire     63
## 421  2020-04-24 North East and Yorkshire     72
## 422  2020-04-25 North East and Yorkshire     69
## 423  2020-04-26 North East and Yorkshire     65
## 424  2020-04-27 North East and Yorkshire     65
## 425  2020-04-28 North East and Yorkshire     57
## 426  2020-04-29 North East and Yorkshire     69
## 427  2020-04-30 North East and Yorkshire     57
## 428  2020-05-01 North East and Yorkshire     64
## 429  2020-05-02 North East and Yorkshire     48
## 430  2020-05-03 North East and Yorkshire     40
## 431  2020-05-04 North East and Yorkshire     49
## 432  2020-05-05 North East and Yorkshire     40
## 433  2020-05-06 North East and Yorkshire     51
## 434  2020-05-07 North East and Yorkshire     45
## 435  2020-05-08 North East and Yorkshire     42
## 436  2020-05-09 North East and Yorkshire     44
## 437  2020-05-10 North East and Yorkshire     40
## 438  2020-05-11 North East and Yorkshire     29
## 439  2020-05-12 North East and Yorkshire     27
## 440  2020-05-13 North East and Yorkshire     28
## 441  2020-05-14 North East and Yorkshire     31
## 442  2020-05-15 North East and Yorkshire     32
## 443  2020-05-16 North East and Yorkshire     35
## 444  2020-05-17 North East and Yorkshire     26
## 445  2020-05-18 North East and Yorkshire     30
## 446  2020-05-19 North East and Yorkshire     27
## 447  2020-05-20 North East and Yorkshire     22
## 448  2020-05-21 North East and Yorkshire     33
## 449  2020-05-22 North East and Yorkshire     22
## 450  2020-05-23 North East and Yorkshire     18
## 451  2020-05-24 North East and Yorkshire     26
## 452  2020-05-25 North East and Yorkshire     21
## 453  2020-05-26 North East and Yorkshire     21
## 454  2020-05-27 North East and Yorkshire     22
## 455  2020-05-28 North East and Yorkshire     21
## 456  2020-05-29 North East and Yorkshire     25
## 457  2020-05-30 North East and Yorkshire     20
## 458  2020-05-31 North East and Yorkshire     20
## 459  2020-06-01 North East and Yorkshire     17
## 460  2020-06-02 North East and Yorkshire     23
## 461  2020-06-03 North East and Yorkshire     23
## 462  2020-06-04 North East and Yorkshire     17
## 463  2020-06-05 North East and Yorkshire     18
## 464  2020-06-06 North East and Yorkshire     21
## 465  2020-06-07 North East and Yorkshire     14
## 466  2020-06-08 North East and Yorkshire     11
## 467  2020-06-09 North East and Yorkshire     12
## 468  2020-06-10 North East and Yorkshire     18
## 469  2020-06-11 North East and Yorkshire      7
## 470  2020-06-12 North East and Yorkshire      9
## 471  2020-06-13 North East and Yorkshire     10
## 472  2020-06-14 North East and Yorkshire     11
## 473  2020-06-15 North East and Yorkshire      9
## 474  2020-06-16 North East and Yorkshire     10
## 475  2020-06-17 North East and Yorkshire      9
## 476  2020-06-18 North East and Yorkshire     10
## 477  2020-06-19 North East and Yorkshire      6
## 478  2020-06-20 North East and Yorkshire      4
## 479  2020-06-21 North East and Yorkshire      4
## 480  2020-06-22 North East and Yorkshire      6
## 481  2020-06-23 North East and Yorkshire      7
## 482  2020-06-24 North East and Yorkshire      9
## 483  2020-06-25 North East and Yorkshire      3
## 484  2020-06-26 North East and Yorkshire      7
## 485  2020-06-27 North East and Yorkshire      3
## 486  2020-06-28 North East and Yorkshire      4
## 487  2020-06-29 North East and Yorkshire      2
## 488  2020-06-30 North East and Yorkshire      1
## 489  2020-03-01               North West      0
## 490  2020-03-02               North West      0
## 491  2020-03-03               North West      0
## 492  2020-03-04               North West      0
## 493  2020-03-05               North West      1
## 494  2020-03-06               North West      0
## 495  2020-03-07               North West      0
## 496  2020-03-08               North West      1
## 497  2020-03-09               North West      0
## 498  2020-03-10               North West      0
## 499  2020-03-11               North West      0
## 500  2020-03-12               North West      2
## 501  2020-03-13               North West      3
## 502  2020-03-14               North West      1
## 503  2020-03-15               North West      4
## 504  2020-03-16               North West      2
## 505  2020-03-17               North West      4
## 506  2020-03-18               North West      6
## 507  2020-03-19               North West      7
## 508  2020-03-20               North West     10
## 509  2020-03-21               North West     11
## 510  2020-03-22               North West     13
## 511  2020-03-23               North West     15
## 512  2020-03-24               North West     21
## 513  2020-03-25               North West     21
## 514  2020-03-26               North West     29
## 515  2020-03-27               North West     36
## 516  2020-03-28               North West     28
## 517  2020-03-29               North West     46
## 518  2020-03-30               North West     67
## 519  2020-03-31               North West     52
## 520  2020-04-01               North West     86
## 521  2020-04-02               North West     96
## 522  2020-04-03               North West     95
## 523  2020-04-04               North West     98
## 524  2020-04-05               North West    102
## 525  2020-04-06               North West    100
## 526  2020-04-07               North West    135
## 527  2020-04-08               North West    127
## 528  2020-04-09               North West    119
## 529  2020-04-10               North West    117
## 530  2020-04-11               North West    138
## 531  2020-04-12               North West    125
## 532  2020-04-13               North West    129
## 533  2020-04-14               North West    131
## 534  2020-04-15               North West    114
## 535  2020-04-16               North West    135
## 536  2020-04-17               North West     98
## 537  2020-04-18               North West    113
## 538  2020-04-19               North West     71
## 539  2020-04-20               North West     83
## 540  2020-04-21               North West     76
## 541  2020-04-22               North West     86
## 542  2020-04-23               North West     85
## 543  2020-04-24               North West     66
## 544  2020-04-25               North West     66
## 545  2020-04-26               North West     55
## 546  2020-04-27               North West     54
## 547  2020-04-28               North West     57
## 548  2020-04-29               North West     63
## 549  2020-04-30               North West     59
## 550  2020-05-01               North West     45
## 551  2020-05-02               North West     56
## 552  2020-05-03               North West     55
## 553  2020-05-04               North West     48
## 554  2020-05-05               North West     48
## 555  2020-05-06               North West     44
## 556  2020-05-07               North West     49
## 557  2020-05-08               North West     42
## 558  2020-05-09               North West     30
## 559  2020-05-10               North West     41
## 560  2020-05-11               North West     35
## 561  2020-05-12               North West     38
## 562  2020-05-13               North West     25
## 563  2020-05-14               North West     26
## 564  2020-05-15               North West     33
## 565  2020-05-16               North West     32
## 566  2020-05-17               North West     24
## 567  2020-05-18               North West     31
## 568  2020-05-19               North West     35
## 569  2020-05-20               North West     27
## 570  2020-05-21               North West     27
## 571  2020-05-22               North West     26
## 572  2020-05-23               North West     31
## 573  2020-05-24               North West     26
## 574  2020-05-25               North West     31
## 575  2020-05-26               North West     27
## 576  2020-05-27               North West     27
## 577  2020-05-28               North West     28
## 578  2020-05-29               North West     20
## 579  2020-05-30               North West     19
## 580  2020-05-31               North West     13
## 581  2020-06-01               North West     12
## 582  2020-06-02               North West     27
## 583  2020-06-03               North West     22
## 584  2020-06-04               North West     22
## 585  2020-06-05               North West     16
## 586  2020-06-06               North West     26
## 587  2020-06-07               North West     20
## 588  2020-06-08               North West     23
## 589  2020-06-09               North West     17
## 590  2020-06-10               North West     16
## 591  2020-06-11               North West     16
## 592  2020-06-12               North West     11
## 593  2020-06-13               North West      9
## 594  2020-06-14               North West     15
## 595  2020-06-15               North West     15
## 596  2020-06-16               North West     13
## 597  2020-06-17               North West     10
## 598  2020-06-18               North West     13
## 599  2020-06-19               North West      7
## 600  2020-06-20               North West     11
## 601  2020-06-21               North West      6
## 602  2020-06-22               North West     11
## 603  2020-06-23               North West     13
## 604  2020-06-24               North West     13
## 605  2020-06-25               North West     14
## 606  2020-06-26               North West      4
## 607  2020-06-27               North West      4
## 608  2020-06-28               North West      6
## 609  2020-06-29               North West      3
## 610  2020-06-30               North West      1
## 611  2020-03-01               South East      0
## 612  2020-03-02               South East      0
## 613  2020-03-03               South East      1
## 614  2020-03-04               South East      0
## 615  2020-03-05               South East      1
## 616  2020-03-06               South East      0
## 617  2020-03-07               South East      0
## 618  2020-03-08               South East      1
## 619  2020-03-09               South East      1
## 620  2020-03-10               South East      1
## 621  2020-03-11               South East      1
## 622  2020-03-12               South East      0
## 623  2020-03-13               South East      1
## 624  2020-03-14               South East      1
## 625  2020-03-15               South East      5
## 626  2020-03-16               South East      8
## 627  2020-03-17               South East      7
## 628  2020-03-18               South East     10
## 629  2020-03-19               South East      9
## 630  2020-03-20               South East     13
## 631  2020-03-21               South East      7
## 632  2020-03-22               South East     25
## 633  2020-03-23               South East     20
## 634  2020-03-24               South East     22
## 635  2020-03-25               South East     29
## 636  2020-03-26               South East     35
## 637  2020-03-27               South East     34
## 638  2020-03-28               South East     36
## 639  2020-03-29               South East     55
## 640  2020-03-30               South East     58
## 641  2020-03-31               South East     65
## 642  2020-04-01               South East     66
## 643  2020-04-02               South East     55
## 644  2020-04-03               South East     72
## 645  2020-04-04               South East     80
## 646  2020-04-05               South East     82
## 647  2020-04-06               South East     88
## 648  2020-04-07               South East    100
## 649  2020-04-08               South East     83
## 650  2020-04-09               South East    104
## 651  2020-04-10               South East     88
## 652  2020-04-11               South East     88
## 653  2020-04-12               South East     88
## 654  2020-04-13               South East     84
## 655  2020-04-14               South East     65
## 656  2020-04-15               South East     72
## 657  2020-04-16               South East     56
## 658  2020-04-17               South East     86
## 659  2020-04-18               South East     57
## 660  2020-04-19               South East     70
## 661  2020-04-20               South East     87
## 662  2020-04-21               South East     51
## 663  2020-04-22               South East     54
## 664  2020-04-23               South East     57
## 665  2020-04-24               South East     64
## 666  2020-04-25               South East     51
## 667  2020-04-26               South East     51
## 668  2020-04-27               South East     40
## 669  2020-04-28               South East     40
## 670  2020-04-29               South East     47
## 671  2020-04-30               South East     29
## 672  2020-05-01               South East     37
## 673  2020-05-02               South East     36
## 674  2020-05-03               South East     17
## 675  2020-05-04               South East     35
## 676  2020-05-05               South East     29
## 677  2020-05-06               South East     25
## 678  2020-05-07               South East     27
## 679  2020-05-08               South East     26
## 680  2020-05-09               South East     28
## 681  2020-05-10               South East     19
## 682  2020-05-11               South East     25
## 683  2020-05-12               South East     27
## 684  2020-05-13               South East     18
## 685  2020-05-14               South East     32
## 686  2020-05-15               South East     24
## 687  2020-05-16               South East     22
## 688  2020-05-17               South East     18
## 689  2020-05-18               South East     22
## 690  2020-05-19               South East     12
## 691  2020-05-20               South East     22
## 692  2020-05-21               South East     15
## 693  2020-05-22               South East     17
## 694  2020-05-23               South East     21
## 695  2020-05-24               South East     17
## 696  2020-05-25               South East     13
## 697  2020-05-26               South East     19
## 698  2020-05-27               South East     18
## 699  2020-05-28               South East     12
## 700  2020-05-29               South East     21
## 701  2020-05-30               South East      8
## 702  2020-05-31               South East     12
## 703  2020-06-01               South East     11
## 704  2020-06-02               South East     13
## 705  2020-06-03               South East     18
## 706  2020-06-04               South East     11
## 707  2020-06-05               South East     11
## 708  2020-06-06               South East     10
## 709  2020-06-07               South East     12
## 710  2020-06-08               South East      8
## 711  2020-06-09               South East     10
## 712  2020-06-10               South East     11
## 713  2020-06-11               South East      5
## 714  2020-06-12               South East      6
## 715  2020-06-13               South East      6
## 716  2020-06-14               South East      7
## 717  2020-06-15               South East      8
## 718  2020-06-16               South East     11
## 719  2020-06-17               South East      8
## 720  2020-06-18               South East      4
## 721  2020-06-19               South East      6
## 722  2020-06-20               South East      5
## 723  2020-06-21               South East      3
## 724  2020-06-22               South East      2
## 725  2020-06-23               South East      8
## 726  2020-06-24               South East      6
## 727  2020-06-25               South East      4
## 728  2020-06-26               South East      7
## 729  2020-06-27               South East      6
## 730  2020-06-28               South East      5
## 731  2020-06-29               South East      2
## 732  2020-06-30               South East      0
## 733  2020-03-01               South West      0
## 734  2020-03-02               South West      0
## 735  2020-03-03               South West      0
## 736  2020-03-04               South West      0
## 737  2020-03-05               South West      0
## 738  2020-03-06               South West      0
## 739  2020-03-07               South West      0
## 740  2020-03-08               South West      0
## 741  2020-03-09               South West      0
## 742  2020-03-10               South West      0
## 743  2020-03-11               South West      1
## 744  2020-03-12               South West      0
## 745  2020-03-13               South West      0
## 746  2020-03-14               South West      1
## 747  2020-03-15               South West      0
## 748  2020-03-16               South West      0
## 749  2020-03-17               South West      2
## 750  2020-03-18               South West      2
## 751  2020-03-19               South West      4
## 752  2020-03-20               South West      3
## 753  2020-03-21               South West      6
## 754  2020-03-22               South West      7
## 755  2020-03-23               South West      8
## 756  2020-03-24               South West      7
## 757  2020-03-25               South West      9
## 758  2020-03-26               South West     11
## 759  2020-03-27               South West     13
## 760  2020-03-28               South West     21
## 761  2020-03-29               South West     18
## 762  2020-03-30               South West     23
## 763  2020-03-31               South West     23
## 764  2020-04-01               South West     22
## 765  2020-04-02               South West     23
## 766  2020-04-03               South West     30
## 767  2020-04-04               South West     42
## 768  2020-04-05               South West     32
## 769  2020-04-06               South West     34
## 770  2020-04-07               South West     39
## 771  2020-04-08               South West     47
## 772  2020-04-09               South West     24
## 773  2020-04-10               South West     46
## 774  2020-04-11               South West     43
## 775  2020-04-12               South West     23
## 776  2020-04-13               South West     27
## 777  2020-04-14               South West     24
## 778  2020-04-15               South West     32
## 779  2020-04-16               South West     29
## 780  2020-04-17               South West     33
## 781  2020-04-18               South West     25
## 782  2020-04-19               South West     31
## 783  2020-04-20               South West     26
## 784  2020-04-21               South West     26
## 785  2020-04-22               South West     23
## 786  2020-04-23               South West     17
## 787  2020-04-24               South West     19
## 788  2020-04-25               South West     15
## 789  2020-04-26               South West     27
## 790  2020-04-27               South West     13
## 791  2020-04-28               South West     17
## 792  2020-04-29               South West     15
## 793  2020-04-30               South West     26
## 794  2020-05-01               South West      6
## 795  2020-05-02               South West      7
## 796  2020-05-03               South West     10
## 797  2020-05-04               South West     17
## 798  2020-05-05               South West     14
## 799  2020-05-06               South West     19
## 800  2020-05-07               South West     16
## 801  2020-05-08               South West      6
## 802  2020-05-09               South West     11
## 803  2020-05-10               South West      5
## 804  2020-05-11               South West      8
## 805  2020-05-12               South West      7
## 806  2020-05-13               South West      7
## 807  2020-05-14               South West      6
## 808  2020-05-15               South West      4
## 809  2020-05-16               South West      4
## 810  2020-05-17               South West      6
## 811  2020-05-18               South West      4
## 812  2020-05-19               South West      6
## 813  2020-05-20               South West      1
## 814  2020-05-21               South West      9
## 815  2020-05-22               South West      6
## 816  2020-05-23               South West      6
## 817  2020-05-24               South West      3
## 818  2020-05-25               South West      8
## 819  2020-05-26               South West     11
## 820  2020-05-27               South West      5
## 821  2020-05-28               South West     10
## 822  2020-05-29               South West      7
## 823  2020-05-30               South West      3
## 824  2020-05-31               South West      2
## 825  2020-06-01               South West      7
## 826  2020-06-02               South West      2
## 827  2020-06-03               South West      7
## 828  2020-06-04               South West      2
## 829  2020-06-05               South West      2
## 830  2020-06-06               South West      1
## 831  2020-06-07               South West      3
## 832  2020-06-08               South West      3
## 833  2020-06-09               South West      0
## 834  2020-06-10               South West      1
## 835  2020-06-11               South West      2
## 836  2020-06-12               South West      2
## 837  2020-06-13               South West      2
## 838  2020-06-14               South West      0
## 839  2020-06-15               South West      1
## 840  2020-06-16               South West      2
## 841  2020-06-17               South West      0
## 842  2020-06-18               South West      0
## 843  2020-06-19               South West      0
## 844  2020-06-20               South West      2
## 845  2020-06-21               South West      0
## 846  2020-06-22               South West      1
## 847  2020-06-23               South West      1
## 848  2020-06-24               South West      1
## 849  2020-06-25               South West      0
## 850  2020-06-26               South West      3
## 851  2020-06-27               South West      0
## 852  2020-06-28               South West      0
## 853  2020-06-29               South West      0
## 854  2020-06-30               South West      0

1.5 Completion date

We extract the completion date from the NHS Pathways file timestamp:


database_date <- attr(x, "timestamp")
database_date
## [1] "2020-07-01"

The completion date of the NHS Pathways data is Wednesday 01 Jul 2020.

1.6 Auxiliary functions

These are functions which will be used further in the analyses.

Function to estimate the generalised R-squared as the proportion of deviance explained by a given model:


## Function to calculate R2 for Poisson model
## not adjusted for model complexity but all models have the same DF here

Rsq <- function(x) {
  1 - (x$deviance / x$null.deviance)
}

Function to extract growth rates per region as well as halving times, and the associated 95% confidence intervals:


## function to extract the coefficients, find the level of the intercept,
## reconstruct the values of r, get confidence intervals

get_r <- function(model) {
  ##  extract coefficients and conf int
  out <- data.frame(r = coef(model))  %>%
    rownames_to_column("var") %>% 
    cbind(confint(model)) %>%
    filter(!grepl("day_of_week", var)) %>% 
    filter(grepl("day", var)) %>%
    rename(lower_95 = "2.5 %",
           upper_95 = "97.5 %") %>%
    mutate(var = sub("day:", "", var))
  
  ## reconstruct values: intercept + region-coefficient
  for (i in 2:nrow(out)) {
    out[i, -1] <- out[1, -1] + out[i, -1]
  }
  
  ## find the name of the intercept, restore regions names
  out <- out %>%
    mutate(nhs_region = model$xlevels$nhs_region) %>%
    select(nhs_region, everything(), -var)
  
  ## find halving times
  halving <- log(0.5) / out[,-1] %>%
    rename(halving_t = r,
           halving_t_lower_95 = lower_95,
           halving_t_upper_95 = upper_95)
  
  ## set halving times with exclusion intervals to NA
  no_halving <- out$lower_95 < 0 & out$upper_95 > 0
  halving[no_halving, ] <- NA_real_
  
  ## return all data
  cbind(out, halving)
  
}

Functions used in the correlation analysis between NHS Pathways reports and deaths:

## Function to calculate Pearson's correlation between deaths and lagged
## reports. Note that `pearson` can be replaced with `spearman` for rank
## correlation.

getcor <- function(x, ndx) {
  return(cor(x$deaths[ndx],
             x$note_lag[ndx],
             use = "complete.obs",
             method = "pearson"))
}

## Catch if sample size throws an error
getcor2 <- possibly(getcor, otherwise = NA)

getboot <- function(x) {
  result <- boot::boot.ci(boot::boot(x, getcor2, R = 1000), 
                           type = "bca")
  return(data.frame(n = sum(!is.na(x$note_lag) & !is.na(x$deaths)),
                    r = result$t0,
                    r_low = result$bca[4],
                    r_hi = result$bca[5]))
}

Function to classify the day of the week into weekend, Monday, and the rest:


## Fn to add day of week
day_of_week <- function(df) {
  df %>% 
    dplyr::mutate(day_of_week = lubridate::wday(date, label = TRUE)) %>% 
    dplyr::mutate(day_of_week = dplyr::case_when(
      day_of_week %in% c("Sat", "Sun") ~ "weekend",
      day_of_week %in% c("Mon") ~ "monday",
      !(day_of_week %in% c("Sat", "Sun", "Mon")) ~ "rest_of_week"
    ) %>% 
      factor(levels = c("rest_of_week", "monday", "weekend")))
}

Custom color palettes, color scales, and vectors of colors:


pal <- c("#006212",
         "#ae3cab",
         "#00db90",
         "#960c00",
         "#55aaff",
         "#ff7e78",
         "#00388d")

age.pal <- viridis::viridis(3,begin = 0.1, end = 0.7)

3 Comparison with deaths time series

3.1 Outline

We want to explore the correlation between NHS Pathways reports and deaths, and assess the potential for reports to be used as an early warning system for disease resurgence.

Death data are publically available. We truncate the time series to avoid bias from reporting delay - we assume a conservative delay of three weeks.

3.2 Lagged correlation

We calculate Pearson’s correlation coefficient between deaths and NHS Pathways notifications using different lags. Confidence intervals are obtained using bootstrap. Note that results were also confirmed using Spearman’s rank correlation.

First we join the NHS Pathways and death data, and aggregate over all England:

## truncate death data for reporting delay
trunc_date <- max(dth$date_report) - delay_max

dth_trunc <- dth %>%
  rename(date = date_report) %>%
  filter(date <= trunc_date) 

## join with notification data
all_data <- x %>% 
  filter(!is.na(nhs_region)) %>%
  group_by(date, nhs_region) %>%
  summarise(count = sum(count, na.rm = T)) %>%
  ungroup %>%
  inner_join(dth_trunc,
             by = c("date","nhs_region"))

all_tot <- all_data %>%
  group_by(date) %>%
  summarise(count = sum(count, na.rm = TRUE),
            deaths = sum(deaths, na.rm = TRUE)) 

We calculate correlation with lagged NHS Pathways reports from 0 to 30 days behind deaths:


## Calculate all correlations + bootstrap CIs
lag_cor <- data.frame()
for (i in 0:30) {
  
  ## lag reports
  summary <- all_tot %>% 
    mutate(note_lag = lag(count, i)) %>%
    ## calculate rank correlation and bootstrap CI
    getboot(.) %>%
    mutate(lag = i)

  lag_cor <- bind_rows(lag_cor, summary)
}

cor_vs_lag <- ggplot(lag_cor, aes(lag, r)) +
  theme_bw() +
  geom_ribbon(aes(ymin = r_low, ymax = r_hi), alpha = 0.2) +
  geom_hline(yintercept = 0, lty = "longdash") +
  geom_point() +
  geom_line() +
  labs(x = "Lag between NHS pathways and death data (days)",
       y = "Pearson's correlation") +
  large_txt
cor_vs_lag


l_opt <- which.max(lag_cor$r)

This analysis suggests that the best lag is 23 days. We then compare and plot the number of deaths reported against the number of NHS Pathways reports lagged by 23 days.


all_tot <- all_tot %>%
  rename(date_death = date) %>%
  mutate(note_lag = lag(count, lag_cor$lag[l_opt]),
         note_lag_c = (note_lag - mean(note_lag, na.rm = T)),
         date_note = lag(date_death,16))

lag_mod <- glm(deaths ~ note_lag, data = all_tot, family = "quasipoisson")

summary(lag_mod)
## 
## Call:
## glm(formula = deaths ~ note_lag, family = "quasipoisson", data = all_tot)
## 
## Deviance Residuals: 
##      Min        1Q    Median        3Q       Max  
## -11.0567   -3.3446   -0.3257    3.8621    6.4158  
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 4.795e+00  5.653e-02   84.83   <2e-16 ***
## note_lag    1.288e-05  5.800e-07   22.21   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## (Dispersion parameter for quasipoisson family taken to be 15.65601)
## 
##     Null deviance: 8243.52  on 60  degrees of freedom
## Residual deviance:  958.51  on 59  degrees of freedom
##   (23 observations deleted due to missingness)
## AIC: NA
## 
## Number of Fisher Scoring iterations: 4

exp(coefficients(lag_mod))
## (Intercept)    note_lag 
##  120.921157    1.000013
exp(confint(lag_mod))
##                  2.5 %     97.5 %
## (Intercept) 108.086338 134.902664
## note_lag      1.000012   1.000014

Rsq(lag_mod)
## [1] 0.8837254

mod_fit <- as.data.frame(predict(lag_mod, type = "link", se.fit = TRUE)[1:2])

all_tot_pred <- 
  all_tot %>%
  filter(!is.na(note_lag)) %>%
  mutate(pred = mod_fit$fit,
         pred.se = mod_fit$se.fit,
         low = exp(pred - 1.96*pred.se),
         hi = exp(pred + 1.96*pred.se))


glm_fit <- all_tot_pred %>% 
    filter(!is.na(note_lag)) %>%
  ggplot(aes(x = note_lag, y = deaths)) +
  geom_point() + 
  geom_line(aes(y = exp(pred))) + 
  geom_ribbon(aes(ymin = low, ymax = hi), alpha = 0.3, col = "grey") +
  theme_bw() +
  labs(y = "Daily number of\ndeaths reported",
       x = "Daily number of NHS Pathways reports") +
  large_txt

glm_fit

4 Supplementary figures

4.1 Serial interval distribution

This is a comparison of gamma versus lognormal distribution for the serial interval used to convert r to R in our analysis. Both distributions are parameterised with mean 4.7 and standard deviation 2.9.

SI_param <- epitrix::gamma_mucv2shapescale(4.7, 2.9/4.7)
SI_distribution <- distcrete::distcrete("gamma", interval = 1,
                                        shape = SI_param$shape,
                                        scale = SI_param$scale, w = 0.5)

SI_distribution2 <- distcrete::distcrete("lnorm", interval = 1,
                                        meanlog = log(4.7),
                                        sdlog = log(2.9), w = 0.5)

SI_dist1 <- data.frame(x = SI_distribution$r(1e5)) 
SI_dist1 <- count(SI_dist1, x) %>%
    ggplot() +
    geom_col(aes(x = x, y = n)) +
    labs(x = "Serial interval (days)", y = "Frequency") +
    scale_x_continuous(breaks = seq(0, 30, 5)) +
    theme_bw()

SI_dist2 <- data.frame(x = SI_distribution2$r(1e5)) 
SI_dist2 <- count(SI_dist2, x) %>%
    ggplot() +
    geom_col(aes(x = x, y = n)) +
    labs(x = "Serial interval (days)", y = "Frequency") +
    scale_x_continuous(breaks = seq(0, 200, 20), limits = c(0, 200)) +
    theme_bw()


ggpubr::ggarrange(SI_dist1,
                  SI_dist2,
                  nrow = 1,
                  labels = "AUTO") 

4.2 Sensitivity analysis - 7 or 21 days moving window

We reproduce the window analysis with either a 7 or 21 days window for sensitivity purposes.

First with the 7 days window:

## set moving time window (1/2/3 weeks)
w <- 7

# create empty df
r_all_sliding_7days <- NULL

## make data for model
x_model_all_moving <- x %>%
  filter(!is.na(nhs_region)) %>% 
  group_by(date, nhs_region) %>%
  summarise(n = sum(count)) 

unique_dates <- unique(x_model_all_moving$date)

for (i in 1:(length(unique_dates) - w)) {
  
  date_i <- unique_dates[i]
  
  date_i_max <- date_i + w
  
  model_data <- x_model_all_moving %>%
    filter(date >= date_i & date < date_i_max) %>%
    mutate(day = as.integer(date - date_i)) %>% 
    day_of_week()
  
  
  mod <- glm(n ~ day * nhs_region + day_of_week,
             data = model_data,
             family = 'quasipoisson')
  
  # get growth rate
  r <- get_r(mod)
  r$w_min <- date_i
  r$w_max <- date_i_max
  
  # combine all estimates
  r_all_sliding_7days <- bind_rows(r_all_sliding_7days, r)
  
}

#serial interval distribution
SI_param = epitrix::gamma_mucv2shapescale(4.7, 2.9/4.7)
SI_distribution <- distcrete::distcrete("gamma", interval = 1,
                                        shape = SI_param$shape,
                                        scale = SI_param$scale,
                                        w = 0.5)

#convert growth rates r to R0
r_all_sliding_7days <- r_all_sliding_7days %>%
  mutate(R = epitrix::r2R0(r, SI_distribution),
         R_lower_95 = epitrix::r2R0(lower_95, SI_distribution),
         R_upper_95 = epitrix::r2R0(upper_95, SI_distribution))
# plot
plot_growth <-
  r_all_sliding_7days %>%
  ggplot(aes(x = w_max, y = r)) +
  geom_ribbon(aes(ymin = lower_95, ymax = upper_95, fill = nhs_region), alpha = 0.1) +
  geom_line(aes(colour = nhs_region)) +
  geom_point(aes(colour = nhs_region)) +
  geom_hline(yintercept = 0, linetype = "dashed") +
  theme_bw() +
  scale_weeks +
  theme(legend.position = "bottom",
        plot.margin = margin(0.5,1,0.5,0.5, "cm")) +
  guides(colour = guide_legend(title = "",override.aes = list(fill = NA)), fill = FALSE) +
  labs(x = "",
       y = "Estimated daily growth rate (r)") +
  scale_colour_manual(values = pal)
plot_R <- r_all_sliding_7days %>%
  ggplot(aes(x = w_max, y = R)) +
  geom_ribbon(aes(ymin = R_lower_95, ymax = R_upper_95, fill = nhs_region), alpha = 0.1) +
  geom_line(aes(colour = nhs_region)) +
  geom_point(aes(colour = nhs_region)) +
  geom_hline(yintercept = 1, linetype = "dashed") +
  theme_bw() +
  scale_weeks +
  theme(legend.position = "bottom",
        plot.margin = margin(0.5,1,0.5,0.5, "cm")) +
  guides(color = guide_legend(title = "", override.aes = list(fill = NA)), fill = FALSE) +
  labs(x = "",
       y = "Estimated effective reproduction\nnumber (Re)") +
  scale_colour_manual(values = pal)

R <- r_all_sliding_7days %>%
  mutate(lower_95 = R_lower_95, 
         upper_95 = R_upper_95,
         value = R,
         measure = "R",
         reference = 1)

r_R <- r_all_sliding_7days %>%
  mutate(measure = "r",
         value = r,
         reference = 0) %>%
  bind_rows(R)

r_R_7 <- r_R %>%
  ggplot(aes(x = w_max, y = value)) +
  geom_ribbon(aes(ymin = lower_95, ymax = upper_95, fill = nhs_region), alpha = 0.1) +
  geom_line(aes(colour = nhs_region)) +
  geom_point(aes(colour = nhs_region)) +
  geom_hline(aes(yintercept = reference), linetype = "dashed") +
  theme_bw() +
  scale_weeks +
  theme(legend.position = "bottom",
        plot.margin = margin(0.5,1,0,0, "cm"),
        strip.background = element_blank(),
        strip.placement = "outside"
  ) +
  guides(color = guide_legend(title = "", override.aes = list(fill = NA)), fill = FALSE) +
  labs(x = "", y = "") +
  scale_colour_manual(values = pal) +
  facet_grid(rows = vars(measure),
             scales = "free_y",
             switch = "y",
             labeller = as_labeller(c(r = "Daily growth rate (r)",
                                      R = "Effective reproduction\nnumber (Re)")))

Then with the 21 days window:

## set moving time window (1/2/3 weeks)
w <- 21

# create empty df
r_all_sliding_21days <- NULL

## make data for model
x_model_all_moving <- x %>%
  filter(!is.na(nhs_region)) %>% 
  group_by(date, nhs_region) %>%
  summarise(n = sum(count)) 

unique_dates <- unique(x_model_all_moving$date)

for (i in 1:(length(unique_dates) - w)) {
  
  date_i <- unique_dates[i]
  
  date_i_max <- date_i + w
  
  model_data <- x_model_all_moving %>%
    filter(date >= date_i & date < date_i_max) %>%
    mutate(day = as.integer(date - date_i)) %>% 
    day_of_week()
  
  
  mod <- glm(n ~ day * nhs_region + day_of_week,
             data = model_data,
             family = 'quasipoisson')
  
  # get growth rate
  r <- get_r(mod)
  r$w_min <- date_i
  r$w_max <- date_i_max
  
  # combine all estimates
  r_all_sliding_21days <- bind_rows(r_all_sliding_21days, r)
  
}

#serial interval distribution
SI_param = epitrix::gamma_mucv2shapescale(4.7, 2.9/4.7)
SI_distribution <- distcrete::distcrete("gamma", interval = 1,
                                        shape = SI_param$shape,
                                        scale = SI_param$scale,
                                        w = 0.5)

#convert growth rates r to R0
r_all_sliding_21days <- r_all_sliding_21days %>%
  mutate(R = epitrix::r2R0(r, SI_distribution),
         R_lower_95 = epitrix::r2R0(lower_95, SI_distribution),
         R_upper_95 = epitrix::r2R0(upper_95, SI_distribution))
# plot
plot_growth <-
  r_all_sliding_21days %>%
  ggplot(aes(x = w_max, y = r)) +
  geom_ribbon(aes(ymin = lower_95, ymax = upper_95, fill = nhs_region), alpha = 0.1) +
  geom_line(aes(colour = nhs_region)) +
  geom_point(aes(colour = nhs_region)) +
  geom_hline(yintercept = 0, linetype = "dashed") +
  theme_bw() +
  scale_weeks +
  theme(legend.position = "bottom",
        plot.margin = margin(0.5,1,0.5,0.5, "cm")) +
  guides(colour = guide_legend(title = "",override.aes = list(fill = NA)), fill = FALSE) +
  labs(x = "",
       y = "Estimated daily growth rate (r)") +
  scale_colour_manual(values = pal)
# plot
plot_R <-
  r_all_sliding_21days %>%
  ggplot(aes(x = w_max, y = R)) +
  geom_ribbon(aes(ymin = R_lower_95, ymax = R_upper_95, fill = nhs_region), alpha = 0.1) +
  geom_line(aes(colour = nhs_region)) +
  geom_point(aes(colour = nhs_region)) +
  geom_hline(yintercept = 1, linetype = "dashed") +
  theme_bw() +
  scale_weeks +
  theme(legend.position = "bottom",
        plot.margin = margin(0.5,1,0.5,0.5, "cm")) +
  guides(color = guide_legend(title = "", override.aes = list(fill = NA)), fill = FALSE) +
  labs(x = "",
       y = "Estimated effective reproduction\nnumber (Re)") +
  scale_colour_manual(values = pal)

R <- r_all_sliding_21days %>%
  mutate(lower_95 = R_lower_95, 
         upper_95 = R_upper_95,
         value = R,
         measure = "R",
         reference = 1)

r_R <- r_all_sliding_21days %>%
  mutate(measure = "r",
         value = r,
         reference = 0) %>%
  bind_rows(R)

r_R_21 <- r_R %>%
  ggplot(aes(x = w_max, y = value)) +
  geom_ribbon(aes(ymin = lower_95, ymax = upper_95, fill = nhs_region), alpha = 0.1) +
  geom_line(aes(colour = nhs_region)) +
  geom_point(aes(colour = nhs_region)) +
  geom_hline(aes(yintercept = reference), linetype = "dashed") +
  theme_bw() +
  scale_weeks +
  theme(legend.position = "bottom",
        plot.margin = margin(0.5,1,0,0, "cm"),
        strip.background = element_blank(),
        strip.placement = "outside"
  ) +
  guides(color = guide_legend(title = "", override.aes = list(fill = NA)), fill = FALSE) +
  labs(x = "", y = "") +
  scale_colour_manual(values = pal) +
  facet_grid(rows = vars(measure),
             scales = "free_y",
             switch = "y",
             labeller = as_labeller(c(r = "Daily growth rate (r)",
                                      R = "Effective reproduction\nnumber (Re)")))

And we combine both outputs into a single plot:


ggpubr::ggarrange(r_R_7,
                  r_R_21,
                  nrow = 2,
                  labels = "AUTO",
                  common.legend = TRUE,
                  legend = "bottom") 

4.3 Correlation between NHS Pathways reports and deaths by NHS region


lag_cor_reg <- data.frame()

for (i in 0:30) {

  summary <-
    all_data %>%
    group_by(nhs_region) %>%
    mutate(note_lag = lag(count, i)) %>%
    ## calculate rank correlation and bootstrap CI for each region
    group_modify(~getboot(.x)) %>%
    mutate(lag = i)
  
  lag_cor_reg <- bind_rows(lag_cor_reg, summary)
}

cor_vs_lag_reg <- 
lag_cor_reg %>%
ggplot(aes(lag, r, col = nhs_region)) +
  geom_hline(yintercept = 0, lty = "longdash") +
  geom_ribbon(aes(ymin = r_low, ymax = r_hi, col = NULL, fill = nhs_region), alpha = 0.2) +
  geom_point() +
  geom_line() +
  facet_wrap(~nhs_region) +
  scale_color_manual(values = pal) +
  scale_fill_manual(values = pal, guide = F) +  
  theme_bw() +
  labs(x = "Lag between NHS pathways and death data (days)", y = "Pearson's correlation", col = "NHS region") +
  theme(legend.position = "bottom") +
  guides(color = guide_legend(override.aes = list(fill = NA)))

cor_vs_lag_reg

5 Export data

We save the tables created during our analysis:


if (!dir.exists("excel_tables")) {
  dir.create("excel_tables")
}


## list all tables, and loop over export
tables_to_export <- c("r_all_sliding", "lag_cor")

for (e in tables_to_export) {
  rio::export(get(e),
              file.path("excel_tables",
                        paste0(e, ".xlsx")))
}

## also export result from regression on lagged data 
rio::export(lag_mod, file.path("excel_tables", "lag_mod.rds"))

6 System information

6.1 Outline

The following information documents the system on which the document was compiled.

6.2 System

This provides information on the operating system.

Sys.info()
##                                                                                            sysname 
##                                                                                           "Darwin" 
##                                                                                            release 
##                                                                                           "19.5.0" 
##                                                                                            version 
## "Darwin Kernel Version 19.5.0: Tue May 26 20:41:44 PDT 2020; root:xnu-6153.121.2~2/RELEASE_X86_64" 
##                                                                                           nodename 
##                                                                                   "Mac-1750.local" 
##                                                                                            machine 
##                                                                                           "x86_64" 
##                                                                                              login 
##                                                                                             "root" 
##                                                                                               user 
##                                                                                           "runner" 
##                                                                                     effective_user 
##                                                                                           "runner"

6.3 R environment

This provides information on the version of R used:

R.version
##                _                           
## platform       x86_64-apple-darwin17.0     
## arch           x86_64                      
## os             darwin17.0                  
## system         x86_64, darwin17.0          
## status                                     
## major          4                           
## minor          0.2                         
## year           2020                        
## month          06                          
## day            22                          
## svn rev        78730                       
## language       R                           
## version.string R version 4.0.2 (2020-06-22)
## nickname       Taking Off Again

6.4 R packages

This provides information on the packages used:

sessionInfo()
## R version 4.0.2 (2020-06-22)
## Platform: x86_64-apple-darwin17.0 (64-bit)
## Running under: macOS Catalina 10.15.5
## 
## Matrix products: default
## BLAS:   /Library/Frameworks/R.framework/Versions/4.0/Resources/lib/libRblas.dylib
## LAPACK: /Library/Frameworks/R.framework/Versions/4.0/Resources/lib/libRlapack.dylib
## 
## locale:
## [1] en_US.UTF-8/en_US.UTF-8/en_US.UTF-8/C/en_US.UTF-8/en_US.UTF-8
## 
## attached base packages:
## [1] stats     graphics  grDevices utils     datasets  methods   base     
## 
## other attached packages:
##  [1] ggnewscale_0.4.1     ggpubr_0.4.0         lubridate_1.7.9     
##  [4] chngpt_2020.5-21     cyphr_1.1.0          DT_0.14             
##  [7] kableExtra_1.1.0     janitor_2.0.1        remotes_2.1.1       
## [10] projections_0.5.1    earlyR_0.0.1         epitrix_0.2.2       
## [13] distcrete_1.0.3      incidence_1.7.1      rio_0.5.16          
## [16] reshape2_1.4.4       rvest_0.3.5          xml2_1.3.2          
## [19] linelist_0.0.40.9000 forcats_0.5.0        stringr_1.4.0       
## [22] dplyr_1.0.0          purrr_0.3.4          readr_1.3.1         
## [25] tidyr_1.1.0          tibble_3.0.1         ggplot2_3.3.2       
## [28] tidyverse_1.3.0      here_0.1             reportfactory_0.0.5 
## 
## loaded via a namespace (and not attached):
##  [1] nlme_3.1-148      fs_1.4.2          webshot_0.5.2     httr_1.4.1       
##  [5] rprojroot_1.3-2   tools_4.0.2       backports_1.1.8   utf8_1.1.4       
##  [9] R6_2.4.1          mgcv_1.8-31       DBI_1.1.0         colorspace_1.4-1 
## [13] withr_2.2.0       gridExtra_2.3     tidyselect_1.1.0  sodium_1.1       
## [17] curl_4.3          compiler_4.0.2    cli_2.0.2         labeling_0.3     
## [21] matchmaker_0.1.1  scales_1.1.1      digest_0.6.25     foreign_0.8-80   
## [25] rmarkdown_2.3     pkgconfig_2.0.3   htmltools_0.5.0   dbplyr_1.4.4     
## [29] htmlwidgets_1.5.1 rlang_0.4.6       readxl_1.3.1      rstudioapi_0.11  
## [33] farver_2.0.3      generics_0.0.2    jsonlite_1.7.0    crosstalk_1.1.0.1
## [37] car_3.0-8         zip_2.0.4         kyotil_2019.11-22 magrittr_1.5     
## [41] Matrix_1.2-18     Rcpp_1.0.4.6      munsell_0.5.0     fansi_0.4.1      
## [45] viridis_0.5.1     abind_1.4-5       lifecycle_0.2.0   stringi_1.4.6    
## [49] yaml_2.2.1        carData_3.0-4     snakecase_0.11.0  MASS_7.3-51.6    
## [53] plyr_1.8.6        grid_4.0.2        blob_1.2.1        crayon_1.3.4     
## [57] lattice_0.20-41   cowplot_1.0.0     splines_4.0.2     haven_2.3.1      
## [61] hms_0.5.3         knitr_1.29        pillar_1.4.4      boot_1.3-25      
## [65] ggsignif_0.6.0    reprex_0.3.0      glue_1.4.1        evaluate_0.14    
## [69] data.table_1.12.8 modelr_0.1.8      vctrs_0.3.1       selectr_0.4-2    
## [73] cellranger_1.1.0  gtable_0.3.0      assertthat_0.2.1  xfun_0.15        
## [77] openxlsx_4.1.5    broom_0.5.6       rstatix_0.6.0     survival_3.1-12  
## [81] viridisLite_0.3.0 ellipsis_0.3.1